Thermophysical properties of paramagnetic Fe from first principles

Abstract

A computationally efficient, yet general, free-energy modeling scheme is developed based on first-principles calculations. Finite-temperature disorder associated with the fast (electronic and magnetic) degrees of freedom is directly included in the electronic structure calculations, whereas the vibrational free energy is evaluated by a proposed model that uses elastic constants to calculate average sound velocity of the quasiharmonic Debye model. The proposed scheme is tested by calculating the lattice parameter, heat capacity, and single-crystal elastic constants of $\ensuremath{\alpha}$-, $\ensuremath{\gamma}$-, and $\ensuremath{\delta}$-iron as functions of temperature in the range 1000--1800 K. The calculations accurately reproduce the well-established experimental data on thermal expansion and heat capacity of $\ensuremath{\gamma}$- and $\ensuremath{\delta}$-iron. Electronic and magnetic excitations are shown to account for about 20% of the heat capacity for the two phases. Nonphonon contributions to thermal expansion are 12% and 10% for $\ensuremath{\alpha}$- and $\ensuremath{\delta}$-Fe and about 30% for $\ensuremath{\gamma}$-Fe. The elastic properties predicted by the model are in good agreement with those obtained in previous theoretical treatments of paramagnetic phases of iron, as well as with the bulk moduli derived from isothermal compressibility measurements [N. Tsujino et al., Earth Planet. Sci. Lett. 375, 244 (2013)]. Less agreement is found between theoretically calculated and experimentally derived single-crystal elastic constants of $\ensuremath{\gamma}$- and $\ensuremath{\delta}$-iron.